New robust stability results for bidirectional associative memory neural networks with multiple time delays

Sibel Senan, Sabri Arik, Derong Liu
2012 Applied Mathematics and Computation  
Equilibrium and stability analysis Bidirectional associative memory neural networks Lyapunov functionals a b s t r a c t In this paper, the robust stability problem is investigated for a class of bidirectional associative memory (BAM) neural networks with multiple time delays. By employing suitable Lyapunov functionals and using the upper bound norm for the interconnection matrices of the neural network system, some novel sufficient conditions ensuring the existence, uniqueness and global
more » ... stability of the equilibrium point are derived. The obtained results impose constraint conditions on the system parameters of neural network independent of the delay parameters. Some numerical examples and simulation results are given to demonstrate the applicability and effectiveness of our results, and to compare the results with previous robust stability results derived in the literature. j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a m c layer, while there are no interconnection among neurons in the same layer. It uses the forward and backward information flow to produce an associative search for stored stimulus-response association. One beneficial characteristic of the BAM is its ability to recall stored pattern pairs in the presence of noise. One may refer to [29] for detailed memory architecture and examples of BAM neural networks. This class of networks has successful application perspective in the field of pattern recognition and artificial intelligence due to its generalization of the single-layer auto-associative Hebbian correlator to a twolayer pattern-matched heteroassociative circuit [30] . Some of these applications require that there should be a well-defined computable solution for all possible initial states. From a mathematical point of view, this means that the equilibrium point of the designed neural network is globally asymptotically stable (GAS). The stability of the BAM neural networks has been extensively studied in the literature in the recent years and many different sufficient conditions ensuring the stability of BAM neural networks have been given in [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] . However, many of the existing stability results derived for the BAM neural networks can be applicable when only a pure delayed neural network model is employed. In recently published papers [44] [45] [46] [47] [48] , a hybrid BAM neural network model in which both instantaneous and delayed signaling occur was considered. In this paper, we study the equilibrium and robust stability properties of hybrid bidirectional associative memory neural networks with multiple time delays. By employing more general types of suitable Lyapunov-Krasovskii functionals and using the upper bound norm for the interconnection matrices of the neural system we obtain some novel delay-independent sufficient conditions for the existence, uniqueness and global robust asymptotic stability of the equilibrium point for hybrid, BAM neural networks with time delays. Some numerical examples are also given to prove that our conditions can be considered as the alternative results to the previous stability results derived in the literature. Model description Dynamical behavior of a hybrid BAM neural network with constant time delays is described by the following set of differential equations [47]:
doi:10.1016/j.amc.2012.04.075 fatcat:atc3af23p5f2daln4h7p5c56ea